Metrohm viva 1.0 (process analysis) - Manual (Page 629)

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5 Method
viva 1.0 (for Process analysis)
￭￭￭￭￭￭￭￭ 617
￭ The variable x is error-
free.
￭ The variable y is
dependent on x and
can be described by the
function y = y(x).
￭ The error with the mea-
surement of y is distrib-
uted normally and is
sufficiently small to be
able to apply linear
error calculation.
Depending on the calibration method selected, the following model func-
tions are available for the calculation of the calibration curve y = y(x):
Selected curve type Calibration func-
tion
Description
Linear regression y = a + bx Line
Quadratic regres-
sion y = a + bx + cx 2 Non-linear curve of
the 2nd degree
Nonlinear regres-
sion y = a + bx + dx 4 Non-linear curve of
the 4th degree
Linear interpola-
tion y = a + bx Line for which all rep-
lications of the two
standard solutions
which are closest in
size to the measured
value of the sample
are taken into
account by the cali-
bration curve.
To calculate the parameters a, b, c and d, one proceeds in accordance
with the Least Squares Fit method, for which the sum of the squared devi-
ations of the measured values y
i
are minimized by the estimates
ŷ
i
. The
scatter σ
y,i
of the measured values is usually not constant, however, but
rather dependent on its value. It is for that reason that the deviations can
be weighted with a factor of g
i
. Extremely scattered values should be
given less weight, more precisely measured values should be weighted
more heavily. It is known from statistics that, under the conditions listed,
weighting 1/variance = 1/standard deviation
2 = 1/( σ
y,i
) 2 yields the best
results. In practice, however, one usually has too few repeated measure-
ments to be able to make estimates from the measured values
σ. A gen-
eral fact is of help here: